A discrete Schrodinger spectral problem and associated evolution equations

Details A discrete Schrodinger spectral problem and associated evolution equations A discrete Schrodinger spectral problem and associated evolution equations

2002-06-11

arxiv.org/abs/nlin/0206012v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

14 pages, LaTeX2e

Scientific paper

10.1088/0305-4470/36/1/309

A recently proposed discrete version of the Schrodinger spectral problem is considered. The whole hierarchy of differential-difference nonlinear evolution equations associated to this spectral problem is derived. It is shown that a discrete version of the KdV, sine-Gordon and Liouville equations are included and that the so called `inverse' class in the hierarchy is local. The whole class of related Darboux and Backlund transformations is also exhibited.

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